2. FACTORIAL DESIGNS F Terms for Factorials F Types of Factorial Designs F Notation for Factorials F Types of Effects F Looking at Tables of Means F Looking at Graphs of Means

3. Terms for Factorials F level: value of an IV F condition: combination of levels of two or more IV’s F factor: another name for IV

4. Factor A Factor B Level 1Level 2 Level 1 Level 2 Level 3 condition

5. Types of Factorial Designs F between subjects F within subjects F mixed

6. Between Subjects B 1 2 A 12 Subjects 1-10 Subjects 11-20 Subjects 31-40 Subjects 21-30

7. Within Subjects B 1 2 A 12 Subjects 1-40 Subjects 1-40 Subjects 1-40 Subjects 1-40

8. Mixed (A Between, B Within) B 1 2 A 12 Subjects 1-20 Subjects 1-20 Subjects 21-40 Subjects 21-40

9. Notation for Factorials F The number of numbers tells you how many i.v.’s F The numbers tell you how many levels F A factorial with two i.v.’s which each have two levels is a 2 x 2

10. Notation for Factorials 2x22x33x4 How many i.v.’s? How many d.v.’s? How many conditions?

11. Types of Effects F Main Effect: the overall effect of one IV, averaging over the levels of the other IV F Interaction: the effect of one IV changes depending on the level of the other IV

12. Drug Therapy 1 2 1 2 40 60 40 mean recovery score No main effect of therapy No main effect of drug BUT the effect of the therapy depends on which drug is being taken

13. Why Factorials? F Reduce amount of non-systematic variance F Ability to measure interaction F Main effects can be misleading without considering the interaction

14. Looking at Means Tables F For main effects: – find marginal means (means of levels) – if marginal means are different, there is a main effect

15. Looking at Means Tables F For interaction: – find simple effects (effects of one variable for each level of other variable) – If simple effects change, there is an interaction

16. A B 1 2 1 2 40 60 40 60 main effect of A 50 4060 +20

17. A B 1 2 1 2 40 60 40 80 4070

18. A B 1 2 1 2 40 30 50 20

19. A B 1 2 1 2 3 50 80

20. Looking at Graphs of Means F main effects: – visually estimate marginal means – if they are at different heights, there is a main effect

21. Looking at Graphs of Means F interaction: – parallel lines mean no interaction – non-parallel lines mean an interaction

22. d.v. 10 20 30 40 50 60 70 0 A 12 B1 B2 x x xx main effect of B

23. d.v. 10 20 30 40 50 60 70 0 A 12 B1 B2

24. d.v. 10 20 30 40 50 60 70 0 A 12 B1 B2

25. d.v. 10 20 30 40 50 60 70 0 A 12 B1 B2

26. d.v. 10 20 30 40 50 60 70 0 A 1 3 B1 B2 2